"From today" sounds like the result of a direct translation from 今日から. I think there's some linguistics word for that sort of thing, but if I ever knew it, I've long forgotten.
Also, shouldn't it be "Let's learn English together..."? Otherwise it's shifting person from first to second while still referring to the same action. The whole phrase structure is off, like @279okshap said, as if it were a direct translation.
"From today" makes it sound like she's talking about present day English as opposed to 1800s English or Middle English, etc. XD I think it would be more direct to say "Today let's learn English together", although she already knows English so the "together" would refer more to the students as a group. There are a lot of more efficient or aesthetically pleasing ways to convey the concept than what's in the picture.
